Projection of images on spherical field
Through kernel-based sampling technology, the pixels of the two-dimensional image slice are projected onto the three-dimensional media plane, solving the problem that traditional systems are difficult to achieve three-dimensional projection and achieving efficient three-dimensional image display effect.
Patent Information
- Application Number
- CN202380083645.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-07-10
- Filing Date
- 2023-11-30
- Publication Date
- 2025-07-11
AI Technical Summary
Existing image projection systems are difficult to effectively convert two-dimensional images into three-dimensional projections on complex three-dimensional media planes, especially on large or three-dimensional visual displays surrounding the audience, with traditional processing capabilities insufficient.
The kernel-based sampling technology is used to project the pixels of the two-dimensional image slice onto the slice of the three-dimensional media plane, and the pixel colors of the three-dimensional media plane are interpolated by weighting and cumulative surrounding pixel color information to realize the three-dimensional projection of the image.
It realizes efficient and realistic image projection on three-dimensional media planes, and can convert and project images in real time or near real time, and is suitable for large venues such as musical theatres, stadiums, etc.
Smart Images

Figure CN120303685A_ABST
Abstract
Description
[0001] Cross - Reference to Related Applications
[0002] This application claims the benefit of priority of U.S. Patent Application No. 18 / 349,323, filed Jul. 10, 2023, which claims the benefit of U.S. Provisional Patent Application No. 63 / 434,366, filed Dec. 21, 2022, and each of these applications is incorporated herein by reference in its entirety. Background Art
[0003] The U.S. media and entertainment industry is the largest in the world. The U.S. media and entertainment industry represents one - third of the global media and entertainment industry, which delivers events such as music events, theater events, sports events, and / or movie events to viewers for their enjoyment. These events typically include an image or a series of images (commonly referred to as video), which can be projected onto a media plane of a venue to enhance the presentation to the audience during the event. Typically, conventional venues include large two - dimensional visual displays (also known as jumbotrons) for displaying these images to the audience. However, as the media plane of the venue becomes more complex, for example, expanding from a large two - dimensional visual display to an even larger three - dimensional visual display surrounding the audience, the traditional processing capabilities for displaying these images on a large two - dimensional visual display are insufficient to display these images on an even larger three - dimensional visual display. Brief Description of the Drawings
[0004] The present disclosure is described with reference to the accompanying drawings. In the drawings, like reference numerals indicate identical or functionally similar elements. Additionally, the left - most one or more digit positions of a reference numeral indicate the drawing in which the reference numeral first appears. In the drawings:
[0005] Figure 1 A simplified block diagram of an exemplary image projection system in accordance with some exemplary embodiments of the present disclosure is illustrated;
[0006] Figure 2A and Figure 2B A simplified block diagram of an exemplary venue in accordance with some exemplary embodiments of the present disclosure is illustrated;
[0007] Figure 3A and Figure 3B An exemplary kernel - based sampling technique that can be implemented within an exemplary projection system in accordance with some exemplary embodiments of the present disclosure is illustrated;
[0008] Figure 4 A flowchart of an exemplary kernel - based sampling technique that can be implemented within an exemplary projection system in accordance with some exemplary embodiments of the present disclosure is illustrated; and
[0009] Figure 5 A simplified block diagram of a computer system for implementing an electronic design platform in accordance with some embodiments of the present disclosure is graphically illustrated.
[0010] The present disclosure will now be described with reference to the accompanying drawings. Detailed Description
[0011] The following disclosure provides many different embodiments or examples for implementing different features of the provided subject matter. Specific examples of components and arrangements are described below to simplify the present disclosure. Of course, these are merely examples and are not intended to be limiting. For example, in the following description, the formation of a first feature above a second feature may include embodiments where the first and second features are formed in direct contact, and may also include embodiments where additional features are formed between the first and second features such that the first and second features may not be in direct contact. Additionally, the present disclosure may repeat reference numerals and / or letters in various examples. This repetition itself does not prescribe a relationship between the various embodiments and / or configurations discussed.
[0012] Overview
[0013] The systems, methods, and apparatuses disclosed herein may retrieve an image or a series of images (commonly referred to as video) that can be projected onto a media plane of a venue. These systems, methods, and apparatuses may convert the image from two dimensions to three dimensions for projection onto the media plane. As part of such conversion, these systems, methods, and apparatuses may logically divide the media plane into multiple slices of the media plane and logically divide the image into multiple slices of the image. Thereafter, these systems, methods, and apparatuses may project one or more pixels of a slice of the media plane onto the image space of an image slice to provide one or more points on the image slice. Thereafter, these systems, methods, and apparatuses weight and accumulate color information of one or more pixels near the one or more points on the image of the image slice to interpolate the color information of the pixels of the media plane.
[0014] Exemplary Image Projection System
[0015] Figure 1 A simplified block diagram of an exemplary image projection system in accordance with some exemplary embodiments of the present disclosure is illustrated. In Figure 1In the exemplary embodiments illustrated, the image projection system 100 may retrieve an image or a series of images (commonly referred to as video) that can be projected onto a media plane of a venue. As will be described in further detail below, the image projection system 100 may convert an image from two dimensions to three dimensions for projection onto a three-dimensional media plane. In some embodiments, the image projection system 100 may logically divide the three-dimensional media plane into multiple slices of the three-dimensional media plane and logically divide the two-dimensional image into multiple slices of the two-dimensional image. In these embodiments, the image projection system 100 may utilize kernel-based sampling techniques to project one or more picture elements (also referred to as pixels) of the three-dimensional slices of the three-dimensional media plane onto the two-dimensional image space of the two-dimensional image slices to provide one or more two-dimensional points on the two-dimensional image slices. In these embodiments, the kernel-based sampling technique then weights and accumulates color information of one or more pixels near the one or more two-dimensional points on the two-dimensional image slice of the image to interpolate the color information of the pixels of the three-dimensional media plane, such as the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model to provide some examples. Exemplary embodiments of the kernel-based sampling technique are further described in U.S. Patent Application No. 18 / 332,874, filed on June 12, 2023, which is incorporated herein by reference in its entirety. As Figure 1 illustrated, the image projection system 100 may include an image recording system 102 that may be communicatively coupled to image processing servers 104.1 to 104.i and the venue 106 via a communication network 108. Although the image projection system 100 is Figure 1 illustrated as including a plurality of discrete devices, one or more of these devices may be combined by those of ordinary skill in the relevant art(s) without departing from the spirit and scope of the present disclosure. For example, the image recording system 102 and one or more of the image processing servers 104.1 to 104.i may be combined into a single discrete device without the communication network 108, which will be apparent to those of ordinary skill in the relevant art(s) without departing from the spirit and scope of the present disclosure.
[0016] The image recording system 102 may store one or more digital image signals. In Figure 1In the exemplary embodiments illustrated, the image recording system 102 can include an image capture system or can be communicatively coupled to an image capture system. Generally, the image capture system can include a camera lens system to project light captured by the camera lens system onto an image sensor. Exemplary embodiments of the image capture system are further described in U.S. Patent Application No. 18 / 332,855, filed on June 12, 2023, which is incorporated herein by reference in its entirety. In some embodiments, one or more digital image signals can be stored by the image recording system 102 as a raw camera image file having radiometric characteristics of the light captured by the image capture system. These radiometric characteristics can include color information for each pixel of the image sensor, such as the luminance and / or chrominance components of the YUV color model and the red, green, and / or blue components of the RGB color model to provide some examples. Alternatively or in addition, the image can be stored by the image recording system 102 in any suitable known image file format that will be clear to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure, such as the Joint Photographic Experts Group (JPEG) image file format, the Exchangeable Image File Format (EXIF), the Tagged Image File Format (TIFF), the Graphics Interchange Format (GIF), the Bitmap Image File (BMP) format, or the Portable Network Graphics (PNG) image file format to provide some examples. In some embodiments, the image recording system 102 can include a machine-readable medium, which can include any mechanism for storing one or more digital image signals in a machine-readable form, such as one or more image processing servers 104.1 to 104.i to provide examples. In these embodiments, the machine-readable medium can include read-only memory (ROM), random access memory (RAM), disk storage media, optical storage media, flash devices, etc. Alternatively or in addition, the machine-readable medium can include, for example, a hard disk drive such as a solid-state drive, a floppy disk drive, and associated removable media, a CD-ROM drive, an optical drive, a flash memory, or a removable media cartridge to persistently store one or more digital image signals.
[0017] The image processing servers 104.1 to 104.i include one or more computer systems to retrieve images stored in the image recording system 102, and exemplary embodiments of the one or more computer systems will be described in further detail below. Alternatively or in addition, the image processing servers 104.1 to 104.i may reconstruct images from one or more digital image signals stored in the image recording system 102. In some embodiments, the image processing servers 104.1 to 104.i may implement one or more digital image processing techniques (also referred to as digital picture processing techniques) to process one or more digital image signals stored in the image recording system 102 to reconstruct images from the one or more digital image signals. In some embodiments, the one or more digital image processing techniques may include decoding, demosaicking, defective pixel removal, white balance, noise reduction, color conversion, tone reproduction, compression, system noise removal, dark frame subtraction, optical correction, contrast processing, unsharp masking, and / or any other suitable well-known digital image processing techniques that will be apparent to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure.
[0018] In Figure 1 the exemplary embodiment illustrated, the image processing servers 104.1 to 104.i may be assigned to different three-dimensional slices of a three-dimensional media plane. The venue 106 will be described in further detail below. In some embodiments, the different three-dimensional slices of the three-dimensional media plane may be associated with different slices of the image. In these embodiments, one or more of the image processing servers among the image processing servers 104.1 to 104.i may assign different three-dimensional slices of the three-dimensional media plane to the image processing servers 104.1 to 104.i and / or associate different three-dimensional slices of the three-dimensional media plane with different slices of the image. After retrieving the image and / or reconstructing the image from one or more digital image signals, the image processing servers 104.1 to 104.i may mathematically transform the two-dimensional coordinates of the slices of the image into the three-dimensional coordinates of the three-dimensional slices of the three-dimensional media plane so that the image can be projected onto the three-dimensional media plane of the venue 106. The image processing servers 104.1 to 104.i operate in a substantially similar manner to each other; thus, for simplicity, the operation of the image processing server 104.1 will be described in further detail below.
[0019] In Figure 1In the exemplary embodiments illustrated, the image processing server 104.1 may utilize kernel-based sampling techniques to mathematically transform the two-dimensional coordinates of corresponding slices of an image into three-dimensional coordinates of corresponding three-dimensional slices of a three-dimensional media plane. In some embodiments, the kernel-based sampling techniques project the pixels of a corresponding three-dimensional slice of the three-dimensional media plane onto the two-dimensional image space of a corresponding slice of the image to effectively transform the pixels of the corresponding three-dimensional slice of the three-dimensional media plane into two-dimensional coordinates of two-dimensional points projected onto the corresponding slice of the image.
[0020] After projecting the three-dimensional coordinates of the corresponding three-dimensional slice of the three-dimensional media plane onto the corresponding slice of the image, the kernel-based sampling techniques statistically interpolate the color information of the corresponding three-dimensional slice of the three-dimensional media plane from the corresponding slice of the image. For example, the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model are provided as some examples. In some embodiments, the kernel-based sampling techniques may statistically interpolate the color information of the pixels of the corresponding three-dimensional slice of the three-dimensional media plane based on the color information of the corresponding slice of the image. In these embodiments, the kernel-based sampling techniques may statistically interpolate the color information of the pixels of the corresponding three-dimensional slice of the three-dimensional media plane by weighting and accumulating the color information of the pixels near the two-dimensional points projected onto the corresponding slice of the image of the corresponding slice of the image.
[0021] After interpolating the color information of the corresponding three-dimensional slice of the three-dimensional media plane, the image processing server 104.1 may provide the color information to the venue 106 to project the corresponding slice of the image onto the venue 106. In some embodiments, the image processing server 104.1 may generate a quadruple for the color information of the corresponding three-dimensional slice of the three-dimensional media plane, the quadruple including the three-dimensional coordinates of the corresponding three-dimensional slice of the three-dimensional media plane and the color information that has been statistically interpolated from the image for the corresponding three-dimensional slice.
[0022] The venue 106 projects the color information of different three-dimensional slices of the three-dimensional media plane provided by the image processing servers 104.1 to 104.i onto the pixels of the different three-dimensional slices of the three-dimensional media plane to project different slices of the image onto the three-dimensional media plane. In some embodiments, the image processing servers 104.1 to 104.i may provide sufficient processing power to the image projection system 100 to project the image onto the three-dimensional media plane in real time or near real time. For example, the image processing servers 104.1 to 104.i may retrieve images at a rate of approximately 24 frames per second. In this example, the image processing servers 104.1 to 104.i may process the images as described above to project the images onto the three-dimensional media plane at a rate of approximately 240 frames per second.
[0023] The communication network 108 communicatively couples the image recording system 102 and the image processing servers 104.1 to 104.i. The communication network 108 can be implemented as a wireless communication network, a wired communication network, and / or any combination thereof that will be apparent to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure. In some embodiments, the communication network 108 can include an optical fiber network or a coaxial cable network that communicatively couples the image recording system 102 to the image processing servers 104.1 to 104.i using optical fibers or coaxial cables. In some embodiments, the communication network 108 can include a hybrid fiber coaxial (HFC) network that combines optical fibers and coaxial cables to communicatively couple the image recording system 102 to the image processing servers 104.1 to 104.i.
[0024] Exemplary Venues That Can Be Implemented within the Exemplary Image Projection System
[0025] Figure 2A and Figure 2B illustrates a simplified block diagram of an exemplary venue in accordance with some exemplary embodiments of the present disclosure. In Figure 2A and Figure 2B the exemplary embodiments illustrated, the venue 200 represents a location for hosting an event. For example, the venue 200 can represent a music venue (e.g., a music theater, a music club, and / or a concert hall), a sports venue (e.g., an arena, a convention center, and / or a stadium), and / or any other suitable venue that will be apparent to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure. The event can include a music event, a theatrical event, a sports event, a movie, and / or any other suitable event that will be apparent to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure. The venue 200 can represent an exemplary embodiment of the venue 106 as described above in Figure 1
[0026] In Figure 2A and Figure 2B In the exemplary embodiments illustrated, the venue 200 may represent a three-dimensional structure, e.g., a hemispherical structure, also known as a hemispherical dome. In some embodiments, the venue 200 may include one or more visual displays (commonly referred to as the three-dimensional media plane 202), which are distributed across the interior or inner arc surface of the venue 200. In these embodiments, the one or more visual displays may include a series of rows and a series of columns of three-dimensional picture elements (also known as pixels) that form the three-dimensional media plane 202. In these embodiments, the pixels may be implemented using one or more light-emitting diode (LED) displays, one or more organic light-emitting diode (OLED) displays, and / or one or more quantum dot (QD) displays to provide some examples. For example, the three-dimensional media plane 202 may include an LED visual display of approximately 16,000 by 16,000, which surrounds the interior of the venue 200 to form a visual display of approximately 160,000 square feet.
[0027] As Figure 2A illustrated, the three-dimensional media plane 202 may be logically divided into three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202. In some embodiments, the three-dimensional slices 204.1 to 204.i may occupy any geometric region of the pixels of the three-dimensional media plane 202, e.g., a rectangular shape. In these embodiments, the any geometric region may include a closed geometric region, such as a regular curve; such as a circle or an ellipse, an irregular curve; a regular polygon, such as an equilateral triangle or a square, and / or an irregular polygon, such as a rectangle and / or a parallelogram to provide some examples. In these embodiments, one or more of the three-dimensional slices 204.1 to 204.i may occupy geometric regions that are similar to each other and / or one or more of the three-dimensional slices 204.1 to 204.i may occupy geometric regions that are not similar to each other. For example, one or more of the three-dimensional slices 204.1 to 204.i may include a similar number of pixels in the three-dimensional media plane 202 with respect to each other and / or one or more of the three-dimensional slices 204.1 to 204.i may occupy a dissimilar number of pixels in the three-dimensional media plane 202 with respect to each other. As described above, the three-dimensional media plane 202 may include a series of rows and a series of columns of pixels. In some embodiments, as Figure 2AAs illustrated, each of the three-dimensional slices from 204.1 to 204.i of the three-dimensional slice may extend along one or more of the series of rows of pixels from the three-dimensional media plane 202 and / or along one or more of the series of columns of pixels from the three-dimensional media plane 202. In these embodiments, one or more of the three-dimensional slices from 204.1 to 204.i may extend along the series of rows of pixels of the three-dimensional media plane 202, from the top or crown of the three-dimensional media plane 202 along one or more columns to the bottom or springing of the three-dimensional media plane 202. In these embodiments, one or more of the three-dimensional slices from 204.1 to 204.i may extend along the series of columns of pixels of the three-dimensional media plane 202, along one or more of the series of rows across the interior or inner arc surface of the three-dimensional media plane 202.
[0028] After the three-dimensional media plane 202 is logically divided into the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202, the three-dimensional slices 204.1 to 204.i may be assigned to the image processing servers 206.1 to 206.i. As Figure 2A illustrated, the image processing servers 206.1 to 206.i may represent exemplary embodiments of the image processing servers 104.1 to 104.i as described above in Figure 1 As Figure 2A illustrated, one or more of the processing servers from the image processing servers 206.1 to 206.i may be assigned to one or more corresponding three-dimensional slices from the three-dimensional slices 204.1 to 204.i. For example, a processing server from the image processing servers 206.1 to 206.i may be assigned to a single three-dimensional slice from the three-dimensional slices 204.1 to 204.i. As another example, a processing server from the image processing servers 206.1 to 206.i may be assigned to multiple three-dimensional slices from the three-dimensional slices 204.1 to 204.i.
[0029] As Figure 2BAs illustrated, the two-dimensional image 208 to be projected onto the three-dimensional media plane 202 can be logically segmented into two-dimensional slices 210.1 to 210.i of the two-dimensional image 208. In some embodiments, the two-dimensional slices 210.1 to 210.i can occupy any geometric region of the pixels of the two-dimensional image 208, such as a rectangular shape. In these embodiments, the any geometric region can include a closed geometric region, such as a regular curve; such as a circle or an ellipse, an irregular curve; a regular polygon, such as an equilateral triangle or a square, and / or an irregular polygon, such as a rectangle and / or a parallelogram to provide some examples. In these embodiments, one or more of the two-dimensional slices 210.1 to 210.i can occupy geometric regions that are similar to each other and / or one or more of the two-dimensional slices 210.1 to 210.i can occupy geometric regions that are not similar to each other. For example, one or more of the two-dimensional slices 210.1 to 210.i can include a similar number of pixels of the two-dimensional image 208 with respect to each other and / or one or more of the two-dimensional slices 210.1 to 210.i can occupy a dissimilar number of pixels of the two-dimensional image 208 with respect to each other.
[0030] After the two-dimensional image 208 is logically segmented into the two-dimensional slices 210.1 to 210.i, three-dimensional slices 204.1 to 204.i can be associated with the two-dimensional slices 210.1 to 210.i. As Figure 2B illustrated, one or more of the three-dimensional slices from among the three-dimensional slices 204.1 to 204.i can be associated with one or more corresponding two-dimensional slices from among the two-dimensional slices 210.1 to 210.i. For example, a three-dimensional slice from among the three-dimensional slices 204.1 to 204.i can be associated with a single two-dimensional slice from among the two-dimensional slices 210.1 to 210.i. As another example, a three-dimensional slice from among the three-dimensional slices 204.1 to 204.i can be associated with multiple two-dimensional slices from among the two-dimensional slices 210.1 to 210.i.
[0031] After the three-dimensional slices 204.1 to 204.i are assigned to the image processing servers 206.1 to 206.i and the three-dimensional slices 204.1 - 204.i are associated with the two-dimensional slices 210.1 to 210.i of the image 208, the image processing servers 206.1 to 206.i can mathematically transform the two-dimensional slices 210.1 to 210.i into the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202 such that the image 202 can be projected onto the three-dimensional media plane 202 of the venue 200, as will be described in further detail below. As will be described in further detail below, the image processing servers 206.1 to 206.i can implement as described above in Figure 1The kernel-based sampling technique described in projects the pixels of the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202 onto the two-dimensional image space of the two-dimensional slices 210.1 to 210.i of the image 208, effectively converting the pixels of the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202 into the two-dimensional coordinates of the two-dimensional points projected onto the two-dimensional slices 210.1 to 210.i of the image 208. In some embodiments, the kernel-based sampling technique may statistically interpolate the color information of the pixels of the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202 based on the color information of the two-dimensional slices 210.1 to 210.i of the image 208. In these embodiments, the kernel-based sampling technique may statistically interpolate the color information of the pixels of the three-dimensional slices 204.1 to 204.i of the three-dimensional media plane 202 by weighting and accumulating the color information of the pixels near the two-dimensional points projected onto the two-dimensional slices 210.1 to 210.i of the image 208.
[0032] Exemplary Kernel-Based Sampling Techniques That Can Be Implemented within the Exemplary Image Projection System
[0033] Figure 3A and Figure 3B illustrates an exemplary kernel-based sampling technique that may be implemented within an exemplary projection system in accordance with some exemplary embodiments of the present disclosure. The following discussion of Figure 3A and Figure 3B will further describe the kernel-based sampling technique as described above in Figure 1 、 Figure 2A and / or Figure 2B . In the exemplary embodiments illustrated in Figure 3A and Figure 3B , the kernel-based sampling technique 300 mathematically transforms the two-dimensional coordinates of an image 302 to the three-dimensional coordinates of a three-dimensional media plane 304 of a site 306. When executed by an image processing server 308, the kernel-based sampling technique 300 may mathematically transform the two-dimensional coordinates of the pixels of the two-dimensional slice 310 of the image 302 to the pixels of the three-dimensional slice 312 of the three-dimensional media plane 304, as will be described in further detail below. In some embodiments, the image processing server 308 may represent one or more of the image processing servers 104.1 to 104.i as described above in Figure 1 and / or one or more of the image processing servers 206.1 to 206.i as described above in Figure 2A and Figure 2B . And the site 306 may represent the site 106 as described above in Figure 1 and / or the site as described above in Figure 2A and Figure 2BExemplary embodiments of the venue 200 described in
[0034] In Figure 3A and Figure 3B In the exemplary embodiments illustrated in Figure 1 and / or Figure 2A the image processing server 308 can be assigned to one or more three-dimensional slices of the three-dimensional media plane 304 in substantially the same manner as described above in Figure 1 and / or Figure 2B such as the three-dimensional slice 312 for example. And, the three-dimensional slice 312 can be associated with one or more two-dimensional slices of the image 302 (such as the two-dimensional slice 310 for example) in substantially the same manner as described above in Figure 1 and / or Figure 2B After the image processing server 308 is assigned to the three-dimensional slice 312 associated with the two-dimensional slice 310, the kernel-based sampling technique 300 can mathematically transform the two-dimensional coordinates of the two-dimensional slice 310 into the three-dimensional coordinates of the three-dimensional slice 312 so that the image 302 can be projected onto the three-dimensional media plane 304. As Figure 3A and Figure 3B illustrated in Figure 3A and Figure 3B the kernel-based sampling technique 300 can project the pixels of the three-dimensional slice 312 onto the two-dimensional space of the two-dimensional slice 310 to effectively transform the pixels into two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310.
[0035] After projecting the pixels of the three-dimensional slice 312, the kernel-based sampling technique 300 statistically interpolates the color information of the pixels of the three-dimensional slice 312 from the pixels of the two-dimensional slice 310, for example, the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model for some examples. In some embodiments, the kernel-based sampling technique 300 can statistically interpolate the color information of the pixels of the three-dimensional slice 312 based on the color information of the pixels of the two-dimensional slice 310. In these embodiments, the kernel-based sampling technique 300 can statistically interpolate the color information of the pixels of the three-dimensional slice 312 by weighting and accumulating the color information of the pixels near the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310.
[0036] As Figure 3A and Figure 3B illustrated in Figure 3A and Figure 3B the kernel-based sampling technique 300 can weight the color information of the pixels near the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310. In some embodiments, the kernel-based sampling technique 300 can identify the pixels near the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310. In these embodiments, the pixels near these two-dimensional points of the two-dimensional slice 310 can be located within a region of interest (ROI) within the two-dimensional slice 310, and the ROI is also referred to as asFigure 3A the sampled kernel space 314 illustrated in Figure 3B and / or the sampled kernel space 316 illustrated in
[0037] In Figure 3A and Figure 3B the exemplary embodiments illustrated in, the kernel-based sampling technique 300 may weight pixels of a statistical interpolation region 318 near two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 within the sampled kernel space 314 and / or the sampled kernel space 316. In some embodiments, the kernel-based sampling technique 300 may implement one or more digital image processing techniques (such as, by way of example, a digital image cropping technique) to generate the statistical interpolation region 318 for statistically interpolating color information of pixels of the three-dimensional slice 312. In these embodiments, the statistical interpolation region 318 includes a first region of pixels of the two-dimensional slice 310 and a second region of pixels of other two-dimensional slices 320 associated with other three-dimensional slices of the three-dimensional media plane assigned to other image processing servers. In some embodiments, the pixels of the other two-dimensional slices 320 may include one or more rows and / or columns of pixels surrounding the periphery of the two-dimensional slice 310 (i.e., adjacent to the two-dimensional slice 310) and / or one or more rows and / or columns of pixels associated with other three-dimensional slices of the three-dimensional media plane assigned to other image processing servers. In these embodiments, depending on the shape of the sampled kernel space 314 and / or the sampled kernel space 316, the pixels of the other two-dimensional slices 320 may include between five (5) and two hundred (200) rows and / or columns of pixels. As Figure 3A illustrated in, the digital image cropping technique may separate the pixels of the two-dimensional slice 310 and the other two-dimensional slices 320 from the image 302 to generate the statistical interpolation region 318. In Figure 3AIn the exemplary embodiments illustrated, pixels near the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 within the sampling kernel space 314 are within the two-dimensional slice 310. In this way, the kernel-based sampling technique 300 can statistically interpolate the color information of the pixels of the three-dimensional slice 312 from the pixels of the two-dimensional slice 310. However, as Figure 3B illustrated, pixels near the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 within the sampling kernel space 316 are within the pixels of the two-dimensional slice 310 and other two-dimensional slices 320. In this way, the kernel-based sampling technique 300 can statistically interpolate the color information of the pixels of the three-dimensional slice 312 from the pixels of the two-dimensional slice 310 and the pixels of other two-dimensional slices 320.
[0038] After identifying the pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316, the kernel-based sampling technique 300 can weight the color information of these pixels, for example, the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model to provide some examples. In some embodiments, the weighting can be a distance-based weighting of the color information of the pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316. For example, pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 that are closer to the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 are weighted more than pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 that are farther from the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310. In some embodiments, if the distance between the pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 and the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 can be considered a random variable, then the kernel-based sampling technique 300 can weight the pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 according to a probability density function, such as a Gaussian distribution, a normal distribution, a standard normal distribution, a Student's t-distribution, a chi-squared distribution, a continuous uniform distribution, and / or any other well-known probability density function that will be clear to those of ordinary skill in the relevant art(s) without departing from the spirit and scope of the present disclosure.
[0039] After the color information of the pixels of the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 has been weighted, the kernel-based sampling technique 300 can accumulate the weighted color information of these pixels to statistically interpolate the color information of the pixels of the three-dimensional slice 312. In Figure 3A and Figure 3BIn the exemplary embodiments illustrated, the kernel-based sampling technique 300 can accumulate color information of pixels in the statistical interpolation region 318 within the sampling kernel space 314 and / or the sampling kernel space 316 that has been weighted as described above to statistically interpolate the color information of the pixels of the three-dimensional slice 312. In these embodiments, the kernel-based sampling technique 300 can associate two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 with the pixels corresponding to these two-dimensional points among the pixels of the three-dimensional slice 312. Thereafter, the kernel-based sampling technique 300 can associate the color information of the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 with the pixels corresponding to these two-dimensional points among the pixels of the three-dimensional slice 312 to statistically interpolate the color information of the pixels of the three-dimensional slice 312. In some embodiments, the kernel-based sampling technique 300 can generate a quadruple for the three-dimensional slice 312, the quadruple including the pixels of the three-dimensional slice 312n and the color information that has been statistically interpolated from the statistical interpolation region 318 for the pixels of the three-dimensional slice 312.
[0040] Figure 4 FIG. illustrates a flow chart of an exemplary kernel-based sampling technique that can be implemented within an exemplary projection system in accordance with some exemplary embodiments of the present disclosure. The present disclosure is not limited to this operation description. Instead, it will be apparent to those of ordinary skill in the relevant art(s) that other operation control flows are also within the scope and spirit of the present disclosure. The following discussion describes an exemplary operation control flow 400 for mathematically transforming the two-dimensional coordinates of the pixels of a slice of an image to the three-dimensional coordinates of a slice of a three-dimensional media plane of a venue (such as the venue 106 described above in Figure 1 as described above in Figure 2A and Figure 2B as described above in Figure 3A and Figure 3B as described above in Figure 1 as described above in Figure 2A and Figure 2B as described above in Figure 3A and Figure 3B as described above in
[0041] At operation 402, the operation control flow 400 projects the pixels of a three-dimensional slice of a three-dimensional media plane onto a two-dimensional slice of a two-dimensional image to effectively convert the pixels of the three-dimensional slice of the three-dimensional media plane into the two-dimensional coordinates of two-dimensional points projected onto the two-dimensional image. In some embodiments, the operation control flow 400 may logically divide the three-dimensional media plane into a plurality of three-dimensional slices of the three-dimensional media plane. In these embodiments, the three-dimensional slices of the three-dimensional media plane may represent one or more of the three-dimensional slices from the plurality of three-dimensional slices of the three-dimensional media plane in a manner substantially similar to that described above in Figure 2A In some embodiments, the operation control flow 400 may logically divide the two-dimensional image into a plurality of two-dimensional slices of the two-dimensional image. In these embodiments, the two-dimensional slices of the two-dimensional image may represent one or more of the two-dimensional slices of the two-dimensional image from the plurality of two-dimensional images in a manner substantially similar to that described above in Figure 2B
[0042] At operation 404, the operation control flow 400 statistically interpolates the color information of the pixels of the three-dimensional slice of the three-dimensional media plane from operation 402 from the pixels of the statistical interpolation region of the two-dimensional image, for example, the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model to provide some examples. In some embodiments, the statistical interpolation region may include the pixels of the two-dimensional slice of the two-dimensional image from operation 402 and the pixels of other two-dimensional slices of the two-dimensional image, where the other two-dimensional slices are derived from the plurality of two-dimensional slices of the two-dimensional image from operation 402, as described above in Figure 3A and Figure 3B In some embodiments, the operation control flow 400 may statistically interpolate the color information of the pixels of the three-dimensional slice of the three-dimensional media plane from operation 402 based on the color information of the pixels of the statistical interpolation region. In these embodiments, the operation control flow 400 may statistically interpolate the color information of the pixels of the three-dimensional slice of the three-dimensional media plane from operation 402 in a manner substantially similar to that described above in Figure 3A and Figure 3B by weighting and accumulating the color information of the pixels near the two-dimensional points projected onto the image from operation 402 of the statistical interpolation region.
[0043] At operation 406, the operation control flow 400 provides the color information of the pixels to the venue for projection onto the venue in a manner substantially similar to that described above in Figure 1 , Figure 2A , Figure 2B , Figure 3A and / or Figure 3B
[0044] Exemplary Computer Systems That Can Be Implemented within the Exemplary Image Projection System
[0045] Figure 5 A simplified block diagram of a computer system for implementing an electronic design platform in accordance with some embodiments of the present disclosure is graphically illustrated. As described above, one or more electronic design software tools may be executed by one or more computing devices, processors, controllers, or other electrical, mechanical, and / or electromechanical devices that will be apparent to those skilled in the relevant art(s) without departing from the spirit and scope of the present disclosure to design, simulate, analyze, and / or verify an architectural design layout of an electronic circuit for an electronic device. The following discussion of Figure 5 will describe a computer system 500 that may be implemented within the image projection system 100 described above in Figure 1 .
[0046] In the embodiment illustrated in Figure 5 , the computer system 500 includes one or more processors 502 to execute as described above in Figure 1One or more electronic design software tools described therein. In some embodiments, one or more processors 502 may include or may be any one of a microprocessor, a graphics processing unit, or a digital signal processor and their electronic processing equivalents (such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA)). As used herein, the term "processor" expresses a tangible data and information processing device that generally physically transforms data and information using sequence transformations (also known as "operations"). The data and information may be physically represented by electrical, magnetic, optical, or acoustic signals that can be stored, accessed, transmitted, combined, compared, or otherwise manipulated by the processor. The term "processor" may express a single processor and a multi-core system or a multi-processor array, including a graphics processing unit, a digital signal processor, a digital processor, or a combination of these elements. The processor may be electronic, for example, including digital logic circuits (e.g., binary logic), or analog (e.g., operational amplifier). The processor may also operate in a "cloud computing" environment or as "software as a service" (SaaS) to support the execution of related operations. For example, at least some of the operations may be performed by a set of processors available at a distributed or remote system, which may be accessed via a communication network (e.g., the Internet) and via one or more software interfaces (e.g., an application programming interface (API)). In some embodiments, the computer system 500 may include an operating system, such as Windows from Microsoft, Solaris from Sun Microsystems, MacOS from Apple Computer, Linux, or UNIX. In some embodiments, the computer system 500 may also include a basic input / output system (BIOS) and processor firmware. The operating system, BIOS, and firmware are used by one or more processors 502 to control the subsystems and interfaces coupled to one or more processors 502. In some embodiments, one or more processors 502 may include Pentium and Itanium from Intel, Opteron and Athlon from Advanced Micro Devices, and ARM processors from ARM Holdings.
[0047] As Figure 5As illustrated in the figure, computer system 500 may include a machine-readable medium 504. In some embodiments, machine-readable medium 504 may further include a main random access memory (“RAM”) 506, a read-only memory (“ROM”) 508, and / or a file storage subsystem 510. RAM 530 may store instructions and data during program execution, and ROM 532 may store fixed instructions. File storage subsystem 510 provides persistent storage for program and data files and may include a hard disk drive, a floppy disk drive and associated removable media, a CD-ROM drive, an optical drive, flash memory, or a removable media cartridge.
[0048] Computer system 500 may further include a user interface input device 512 and a user interface output device 514. User interface input device 512 may include an alphanumeric keyboard, a keypad, a pointing device such as a mouse, trackball, touchpad, stylus, or graphics tablet, a scanner, a touchscreen integrated into a display, an audio input device such as a voice recognition system or a microphone, eye gaze recognition, brain wave pattern recognition, and other types of input devices to provide some examples. User interface input device 512 may be connected to computer system 500 either wired or wirelessly. Generally, user interface input device 512 is intended to include all possible types of devices and ways to input information into computer system 500. User interface input device 512 typically allows a user to identify objects, icons, text, etc. that appear on some type of user interface output device (e.g., a display subsystem). User interface output device 520 may include a display subsystem, a printer, a fax machine, or a non-visual display such as an audio output device. The display subsystem may include a cathode ray tube (CRT), a flat panel device such as a liquid crystal display (LCD), a projection device, or some other device for creating a visible image, such as a virtual reality system. The display subsystem may also provide a non-visual display via, for example, an audio output or a haptic output (e.g., vibration) device. Generally, user interface output device 520 is intended to include all possible types of devices and ways to output information from computer system 500.
[0049] The computer system 500 may further include a network interface 516 to provide an interface to an external network (including an interface to a communication network 518), and is coupled via the communication network 518 to a corresponding interface device of other computer systems or machines. The communication network 518 may include a number of interconnected computer systems, machines, and communication links. These communication links may be wired links, optical links, wireless links, or any other device for the communication of information. The communication network 518 may be any suitable computer network, such as a wide area network such as the Internet and / or a local area network such as Ethernet. The communication network 518 may be wired and / or wireless, and the communication network may use encryption and decryption methods, such as those available for a virtual private network (VNP). The communication network uses one or more communication interfaces, which may receive data from other systems and send data to other systems. Examples of communication interfaces typically include Ethernet network cards, modems (e.g., telephone, satellite, cable, or ISDN), (asynchronous) digital subscriber line (DSL) units, FireWire interfaces, USB interfaces, and the like. One or more communication protocols may be used, such as HTTP, TCP / IP, RTP / RTSP, IPX, and / or UDP.
[0050] As Figure 5 Illustrated, one or more processors 502, machine-readable media 504, user interface input devices 512, user interface output devices 514, and / or network interfaces 516 may be communicatively coupled to each other using a bus subsystem 520. Although the bus subsystem 520 is schematically shown as a single bus, alternative embodiments of the bus subsystem may use multiple buses. For example, a RAM-based main memory may communicate directly with a file storage system using a direct memory access (“DMA”) system.
[0051] Conclusion
[0052] The detailed description illustrates exemplary embodiments consistent with the present disclosure with reference to the accompanying drawings. References in the present disclosure to “exemplary embodiments” indicate that the described exemplary embodiments may include a particular feature, structure, or characteristic, but each exemplary embodiment does not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same exemplary embodiment. Further, any feature, structure, or characteristic described in connection with an exemplary embodiment may be included independently or in any combination with other features, structures, or characteristics of other exemplary embodiments (whether or not explicitly described), whether or not explicitly described.
[0053] The detailed description is not intended to be limiting. On the contrary, the scope of the present disclosure is defined only in accordance with the following claims and their equivalents. It should be understood that the detailed description section (rather than the abstract section) is intended to be used for interpreting the claims. The abstract section may set forth one or more (but not all) exemplary embodiments of the present disclosure, and thus is not intended to limit the present disclosure and the following claims and their equivalents in any way.
[0054] The exemplary embodiments described within the present disclosure have been provided for illustrative purposes and are not intended to be limiting. Other exemplary embodiments are possible and modifications to the exemplary embodiments may be made while remaining within the spirit and scope of the present disclosure. The present disclosure has been described by means of functional building blocks that illustrate the implementation of specified functions and their relationships. For convenience of description, the boundaries of these functional building blocks have been arbitrarily defined herein. Alternative boundaries may be defined as long as the specified functions and their relationships are appropriately performed.
[0055] Embodiments of the present disclosure may be implemented in hardware, firmware, software applications, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing circuit). For example, a machine-readable medium may include a non-transitory machine-readable medium such as read-only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash devices, etc. As another example, a machine-readable medium may include a transitory machine-readable medium such as electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.). Further, firmware, software applications, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are for convenience only and that such actions are actually generated from a computing device, processor, controller, or other device that executes the firmware, software application, routine, instructions, etc.
[0056] The detailed description of the exemplary embodiments fully reveals the generality of the present disclosure, such that others may, by applying the knowledge of those skilled in the relevant art(s), without undue experimentation, readily modify and / or adapt such exemplary embodiments for various applications without departing from the spirit and scope of the present disclosure. Accordingly, such adaptations and modifications are intended to be within the meaning and plurality of equivalents of the exemplary embodiments based on the teachings and guidance presented herein. It should be understood that the language or terminology herein is for the purpose of description and not of limitation, such that the terminology or language of this specification will be interpreted by those skilled in the relevant art(s) in light of the teachings herein.
Claims
1. An image processing server for transforming an image for projection onto a media plane of a venue, the image processor comprising: a memory configured to store instructions; and a processor configured to execute the instructions, which when executed by the processor configure the processor to: project three-dimensional coordinates of a plurality of pixels of a three-dimensional slice of the media plane that is assigned to the image processing server among a plurality of three-dimensional slices of the media plane onto two-dimensional coordinates of a two-dimensional slice of the image that is associated with the three-dimensional slice to provide a plurality of two-dimensional points, interpolate color information of the plurality of pixels of the three-dimensional slice of the media plane based on color information of a first plurality of pixels within the two-dimensional slice of the image that is associated with the three-dimensional slice of the media plane and color information of a second plurality of pixels of the image surrounding the two-dimensional slice, and provide the color information of the plurality of pixels of the three-dimensional slice of the media plane to the venue to project the two-dimensional slice of the image onto the three-dimensional media plane.
2. The image processing server according to claim 1, wherein the instructions when executed by the processor further configure the processor to: logically divide the media plane into the plurality of three-dimensional slices of the media plane; and assign the plurality of three-dimensional slices of the media plane to a plurality of image processing servers.
3. The image processing server according to claim 2, wherein the instructions when executed by the processor further configure the processor to: logically divide the image into the plurality of two-dimensional slices of the image; and associate the plurality of two-dimensional slices of the image with the plurality of three-dimensional slices of the media plane.
4. The image processing server according to claim 1, wherein the instructions when executed by the processor further configure the processor to crop the image to generate a statistical interpolation region of the image, the statistical interpolation region including the first plurality of pixels and the second plurality of pixels.
5. The image processing server according to claim 1, wherein the second plurality of pixels are within a second two-dimensional slice of the plurality of two-dimensional slices of the image, the second two-dimensional slice being associated with a second three-dimensional slice of the plurality of three-dimensional slices of the media plane, the second three-dimensional slice being assigned to a second image processing server among the plurality of image processing servers.
6. The image processing server according to claim 1, wherein the instructions when executed by the processor configure the processor to interpolate the color information of the plurality of pixels of the three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located within a sample kernel space.
7. The image processing server according to claim 6, wherein when executed by the processor, the instructions configure the processor to weight the color information of the first plurality of pixels located within the sample kernel space and the color information of the second plurality of pixels according to a probability density function.
8. A method for operating an image processing server to transform an image for projection onto a media plane of a venue, the method comprising: projecting, by the image processing server, three-dimensional coordinates of a plurality of pixels of a three-dimensional slice of the media plane assigned to the image processing server among a plurality of three-dimensional slices of the media plane onto two-dimensional coordinates of a two-dimensional slice of the image associated with the three-dimensional slice of the image to provide a plurality of two-dimensional points; interpolating, by the image processing server, color information of the plurality of pixels of the three-dimensional slice of the media plane based on color information of a first plurality of pixels within the two-dimensional slice of the image associated with the three-dimensional slice of the media plane and color information of a second plurality of pixels of the image surrounding the two-dimensional slice; and providing, by the image processing server, the color information of the plurality of pixels of the three-dimensional slice of the media plane to the venue to project the two-dimensional slice of the image onto the three-dimensional media plane.
9. The method according to claim 8, further comprising: logically dividing the media plane into the plurality of three-dimensional slices of the media plane; and assigning the plurality of three-dimensional slices of the media plane to a plurality of image processing servers.
10. The method according to claim 9, further comprising: logically dividing the image into the plurality of two-dimensional slices of the image; and associating the plurality of two-dimensional slices of the image with the plurality of three-dimensional slices of the media plane.
11. The method according to claim 8, wherein when executed by the processor, the instructions further configure the processor to crop the image to generate a statistical interpolation region of the image, the statistical interpolation region including the first plurality of pixels and the second plurality of pixels.
12. The method according to claim 8, wherein the second plurality of pixels are within a second two-dimensional slice of the plurality of two-dimensional slices of the image, the second two-dimensional slice being associated with a second three-dimensional slice of the plurality of three-dimensional slices of the media plane, the second three-dimensional slice being assigned to a second image processing server among a plurality of image processing servers.
13. The method according to claim 8, wherein the interpolation includes interpolating the color information of the plurality of pixels of the three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located within a sample kernel space.
14. The method according to claim 13, wherein the interpolation further comprises weighting the color information of the first plurality of pixels located within the sample kernel space and the color information of the second plurality of pixels according to a probability density function.
15. An image projection system for converting an image for projection onto a media plane of a venue, the system comprising: a first image processing server among a plurality of image processing servers, the first image processing server being configured to: project the three-dimensional coordinates of the plurality of pixels of a first three-dimensional slice of the media plane assigned to the first image processing server among the plurality of three-dimensional slices of the media plane onto the two-dimensional coordinates of a first two-dimensional slice associated with the first three-dimensional slice of the plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points, interpolate the color information of the plurality of pixels of the first three-dimensional slice of the media plane based on the color information of a first plurality of pixels within the first two-dimensional slice of the image associated with the first three-dimensional slice of the media plane and the color information of a second plurality of pixels surrounding the first two-dimensional slice of the image, and provide the color information of the plurality of pixels of the first three-dimensional slice of the media plane to the venue to project the first two-dimensional slice of the image onto the three-dimensional media plane; and a second image processing server among a plurality of image processing servers, the first image processing server being configured to: project the three-dimensional coordinates of the plurality of pixels of a second three-dimensional slice of the media plane assigned to the second image processing server among the plurality of three-dimensional slices of the media plane onto the two-dimensional coordinates of a second two-dimensional slice associated with the second three-dimensional slice of the plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points, interpolate the color information of the plurality of pixels of the second three-dimensional slice of the media plane based on the color information of a third plurality of pixels within the second two-dimensional slice of the image associated with the second three-dimensional slice of the media plane and the color information of a fourth plurality of pixels surrounding the second two-dimensional slice of the image, and provide the color information of the plurality of pixels of the second three-dimensional slice of the media plane to the venue to project the second two-dimensional slice of the image onto the three-dimensional media plane.
16. The system according to claim 15, wherein the first image processing server is further configured to: logically divide the media plane into the plurality of three-dimensional slices of the media plane; and assign the second three-dimensional slice of the media plane to the second image processing server.
17. The system according to claim 16, wherein the first image processing server is further configured to: logically divide the image into the plurality of two-dimensional slices of the image; and associate the second two-dimensional slice of the image with the second three-dimensional slice of the media plane.
18. The system according to claim 15, wherein the first image processing server is further configured to crop the image to generate a statistical interpolation region of the image, the statistical interpolation region including the first plurality of pixels and the second plurality of pixels.
19. The system according to claim 15, wherein The second plurality of pixels are within the second two-dimensional slice of the image.
20. The system according to claim 15, wherein the first image processing server is further configured to interpolate the color information of the plurality of pixels of the first three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located within the sample kernel space.
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